Question

An arrangement of spring, strings, pulley and masses is shown in the figure. The pulley and the strings are massless and $M>m$. The spring is light with spring constant $k$. If the string connecting $m$ to the ground is detached, then immediately after detachment

• A. the magnitude of the acceleration of $m$ is zero and that of $M$ is $g$
• B. the magnitude of the acceleration of $m$ is $(M-m)g/m$ and that of $M$ is zero
• C. the accelerations of both masses are same
• D. the elongation in the spring is $(M-m)g/k$

Answer 1

The correct option is B the magnitude of the acceleration of $m$ is $(M-m)g/m$ and that of $M$ is zero

Explanation:
After string attached to ground is cut:
Acceleration of ${}^{\prime }{m}^{\prime }$ we get by the equation,

$a=\frac{T-mg}{m}=\frac{(M-m)g}{m}$ $(T=Mg)$

Acceleration of ${}^{\prime }{M}^{\prime }$,
$a=\frac{Mg-Mg}{m}=0$

Also here the $M$ is attached to the spring and spring dosent show instant reaction on the force and so immediately after the string is cut the mass $M$ will be in rest.